Data processing device

ABSTRACT

A certification device  101  encrypts a feature vector for registration by using a random number and a public key which is set to correspond to a secret key in a decryption device  103 . The encrypted feature vector for registration is registered in an authentication device  102 . In authentication, the certification device encrypts a feature vector for authentication by using the public key and a random number. With the two encrypted feature vectors being kept encrypted, the authentication device generates encrypted similarity degree information from which the decryption device can derive the similarity degree between the two feature vectors by a decryption process using the secret key. The decryption device  103  decrypts the encrypted similarity degree information to derive the similarity degree of the plaintext. The authentication device  102 , if the similarity degree is equal to or larger than a threshold, determines that the user is the correct user. The similarity degree can be derived without using the feature vector of the plaintext. Thus, secure identity authentication with a lower possibility of plaintext theft can be realized.

TECHNICAL FIELD

The present invention relates to an authentication technique in whichidentity authentication is carried out, by using biometric informationor the like.

BACKGROUND ART

Biometric authentication such as fingerprint authentication or veinauthentication is a personal identification method which utilizes adifference in individual fingerprint pattern or individual vein shape.

In recent years, biometric authentication is employed in accessmanagement such as entry/exit management of a building, log-inmanagement of a personal computer, and identity authentication at a bankATM (Automated Teller Machine).

In biometric authentication, authentication is generally performedbetween a user (a person to be authenticated or certified) and anauthentication device (authenticator) in the following manner.

In the registration step, the user registers his or her biometricinformation with the authentication device in advance.

In authentication, the user presents his/her biometric information tothe authentication device.

The authentication device collates the presented biometric informationwith the registered biometric information. If the similarity degreebetween the two pieces of information satisfies a certain condition, theauthentication device determines that the user is the correct user. Ifnot, the authentication device determines that the user is a differentperson.

In this biometric authentication, it is desired that the biometricinformation be protected since it is privacy information that ischaracteristic of an individual.

Hence, a method of performing biometric authentication without revealingthe biometric information itself has been proposed (for example, PatentLiterature 1). According to this method, in registration, encryptedbiometric information is registered, and in authentication, encryptedbiometric information is collated.

As an encryption algorithm that can be used for encryption of biometricinformation, for example, encryption algorithms disclosed in Non-PatentLiteratures 1 to 4 are available.

CITATION LIST Patent Literature

Patent Literature 1: JP 2008-521025

Non-Patent Literature

Non-Patent Literature 1: T. Okamoto, K. Takashima, “Homomorphicencryption and signatures from vector decomposition”, Pairing 2008,Lecture Notes in Computer Science, Vol. 5209, pp. 57-74, 2008.

Non-Patent Literature 2: D. Boneh, E. -J. Goh, K. Nissim, “Evaluating2-DNF formulas on ciphertexts”, Theory Of Cryptography Conference,Lecture Notes in Computer Science, Vol. 3378, pp. 325-341, 2005.

Non-Patent Literature 3: C. Gentry, “Fully homomorphic encryption usingideal lattices”, ACM Symposium on Theory Of Computing, pp. 169-178,2009.

Non-Patent Literature 4: D. Freeman, M. Scott, E. Teske, “A taxonomy ofpairing-friendly elliptic curves”, Journal Of Cryptology, June 2009.

SUMMARY OF INVENTION Technical Problem

In Patent Literature 1, biometric information is protected by encryptionutilizing a public key encryption technique. When encrypting thebiometric information, an ordinary homomorphic encryption such as aPaillier encryption or ElGamal encryption is used as the encryptionalgorithm.

An ordinary homomorphic encryption is an encryption with which aciphertext of the sum of original plaintexts can be calculated from aplurality of ciphertexts. For example, using T pieces of ciphertextsE(x₁), E(x₂), . . . , E(x_(T)), a ciphertext E(x₁+x₂+ . . . +x_(T)) maybe calculated.

Note that E(x₁) represents the ciphertext of x₁ generated using acertain public key.

In the above case, addition is taken as an example. To define precisely,the ordinary homomorphic encryption mentioned above is an encryptionwith which a ciphertext formed by subjecting an original plaintext to acertain type of arithmetic operation can be calculated from a pluralityof ciphertexts.

The type of arithmetic operation includes addition, multiplication, andthe like on a finite field. In any case, one encryption is capable ofonly one type of arithmetic operation.

With the ordinary homomorphic encryption as mentioned above, however, inthe calculation process of authentication, the entire process cannot becompleted with encrypted biometric information alone. The processincludes a portion that needs plaintext biometric information.

For example, with the authentication method described in PatentLiterature 1, the hamming distance of the feature vectors generated frombiometric information (that is, the hamming distance between bit stringsthat constitute the vectors) is employed as the index of similaritydegree checking, and secrecy collation process is performed in thefollowing procedure.

Note that the user does not access the authentication device directly,but accesses the certification device. The certification devicecommunicates with the authentication device, and performs theregistration process and authentication process of the biometricinformation.

Namely, a more general biometric authentication scheme including remotelog-in which uses biometric information is supposed.

Also note that encryption is performed by using a public key that iscommon to the entire system.

In registration, the certification device extracts biometric informationfrom the user, and constitutes a feature vector representing the usercharacteristics, from the extracted biometric information.

Assume that the feature vector is a bit string X=(x₁, x₂, . . . ,x_(T)).

Using a Paillier encryption, the certification device encrypts each bitof the extracted feature vector, calculates an encrypted bit stringE(X)=(E(x₁), E(x₂), . . . , E(x_(T))), sends the encrypted bit stringcalculated to the authentication device, and registers the encrypted bitstring calculated, in the authentication device.

In authentication, the certification device extracts a biometricinformation. bit string Y=(y₁, y₂, . . . , y_(T)) from the user in thesame manner as in registration.

Then, the certification device receives the encrypted bit stringE(X)=(E(x₁), E(x₂), . . . , E(x_(T))) registered, from theauthentication device.

When calculating the ciphertext indicating the hamming distance d_(H)(X,Y) between the bit strings X and Y, the certification device employs thefollowing property (Numeric Expression 1) of the homomorphic encryption.

$\begin{matrix}\begin{matrix}{{E\left( {d_{H}\left( {X,Y} \right)} \right)} = {\prod\limits_{i = 1}^{T}{E\left( {x_{i}^{2} - {2x_{i}y_{i}} + y_{i}^{2}} \right)}}} \\{= {\sum\limits_{i = 1}^{T}{E\left( {x_{i} - {2x_{i}y_{i}} + y_{i}} \right)}}} \\{= {\sum\limits_{i = 1}^{T}{{E\left( x_{i} \right)}{E\left( y_{i} \right)}{E\left( x_{i} \right)}^{{- 2}{yi}}}}}\end{matrix} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 1} \right\rbrack\end{matrix}$

The second expression is converted into the third expression, becauseeach of x₁ and y₁ takes no other value but 0 or 1.

The third expression is converted into the fourth expression, becausethe Paillier encryption is an ordinary homomorphic encryption having aproperty with which a ciphertext of the sum of the original plaintextscan be obtained from the product of the ciphertexts.

Utilizing this property and employing the encrypted bit stringE(X)=(E(x₁), E(x₂), . . . , E(x_(T))) received from the authenticationdevice and the biometric information bit string Y=(y₁, y₂, . . . ,y_(T)), the certification device calculates the following value(Numerical Expression 2), and sends the obtained value to theauthentication device.

$\begin{matrix}{\prod\limits_{i = 1}^{T}{{E\left( y_{i} \right)}{E\left( x_{i} \right)}^{{- 2}\; y\; i}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 2} \right\rbrack\end{matrix}$

The authentication device multiplies the received value by the followingvalue (Numerical Expression 3), thus calculating an encryption hammingdistance E(d_(H)(X, Y)).

Using a secure protocol, the hamming distance is decrypted, andsimilarity degree checking is performed.

$\begin{matrix}{\prod\limits_{i = 1}^{T}{E\left( x_{i} \right)}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 3} \right\rbrack\end{matrix}$

As described above, with an ordinary homomorphic encryption such as aPaillier encryption, when calculating a ciphertext −2x_(i)y_(i), acalculation E(x_(i))^(−2yi) is performed. Thus, a plaintext y_(i) isneeded in the exponential part.

In other words, the entire process cannot be performed with only theciphertext because of the property of the homomorphic encryption.

For this reason, the authentication device must send the encryptedbiometric information E(x)=(E(x₁), E(x₂), . . . , E(x_(T))) to thecertification device once, and the certification device must performcalculation using the plaintext y_(i).

In sending of the encrypted biometric information, in the case ofso-called 1:1 authentication where the authentication-target user isseparately specified by ID information or the like, it suffices ifencrypted biometric information for one person is sent. In the case ofso-called 1:N authentication where the authentication-target user is notspecified and collation with many users stored in the database isrequired, it is necessary to send encrypted biometric information innumber of pieces proportional to the number of users.

Consequently, there is a problem in that the communication amountbetween the authentication device and the certification device increasesin proportion to the number of users.

It is also desired from the viewpoint of security that the plaintextbiometric information be deleted from the certification device as soonas possible.

As described above, however, since the plaintext biometric informationis required for authentication, in 1:N authentication particularly, thebiometric information on a terminal cannot be deleted untilauthentication is completed, so there is a problem in that the biometricinformation will be exposed to the risk of theft for a longer period oftime.

It is one of the major objects of the present invention to solve theabove problems. The major object of the present invention is to renderunnecessary a plaintext that has been required in the course ofauthentication process, and to diminish the risk of plaintext theft,thus providing a more secure secrecy collating method.

It is another object of the present invention is to decrease thecommunication amount between the authentication device and thecertification device.

Solution to Problem

A data processing device according to the present invention includes:

a public key storage part which stores a public key generated in adecryption device based on a doubly homomorphic encryption algorithm anddistributed by the decryption device;

an encrypted data storage part which stores, as encrypted first data,first data that has been encrypted by an encryption device which holdsthe public key distributed by the decryption device, by using the publickey held in the encryption device;

an encrypted data input part which, after the encrypted first data isstored in the encrypted data storage part, inputs, as encrypted seconddata, second data that has been encrypted by the encryption device byusing the public key held in the encryption device;

a random number generating part which generates a random number by usingat least a part of the public key; and

an encrypted similarity degree generating part which performscomputation on the encrypted first data and the encrypted second data byusing the public key stored in the public key storage part and therandom number generated by the random number generating part, andgenerates, as encrypted similarity degree information, encryptedinformation from which a similarity degree between the first data andthe second data can be derived by a decryption process using a secretkey generated to correspond to the public key, with the encrypted firstdata and the encrypted second data being kept encrypted.

Advantageous Effects of Invention

According to the present invention, with both the encrypted first dataand the encrypted second data being kept in the encrypted state, theencrypted similarity degree information from which the similarity degreebetween the first data and the second data can be derived by adecryption process using the secret key generated to correspond to thepublic key, is generated. The similarity degree between the first dataand the second data can be derived without using the first data and thesecond data which are plaintexts. Thus, secure identity authenticationwith a lower possibility of plaintext theft can be realized.

BRIEF DESCRIPTION OF DRAWINGS

[FIG. 1] is a diagram showing a configuration of a biometricauthentication system according to Embodiment 1.

[FIG. 2] is a diagram showing a configuration of a certification deviceaccording to Embodiment 1.

[FIG. 3] is a diagram showing a configuration of an authenticationdevice according to Embodiment 1.

[FIG. 4] is a diagram showing a configuration of a decryption deviceaccording to Embodiment 1.

[FIG. 5] is a flowchart showing an example of a setup process accordingto Embodiment 1.

[FIG. 6] is a flowchart showing an example of a biometric informationregistration process according to Embodiment 1.

[FIG. 7] is a flowchart showing an example of an authentication processaccording to Embodiment 1.

[FIG. 8] is a flowchart showing the example of the authenticationprocess according to Embodiment 1.

[FIG. 9] is a flowchart showing the example of the authenticationprocess according to Embodiment 1.

[FIG. 10] is a flowchart showing an example of a biometric informationregistration process according to Embodiment 2.

[FIG. 11] is a flowchart showing an example of an authentication processaccording to Embodiment 2.

[FIG. 12] is a flowchart showing the example of the authenticationprocess according to Embodiment 2.

[FIG. 13] is a flowchart showing an example of a setup process accordingto Embodiment 3.

[FIG. 14] is a flowchart showing an example of a biometric informationregistration process according to Embodiment 3.

[FIG. 15] is a flowchart showing an example of an authentication processaccording to Embodiment 3.

[FIG. 16] is a flowchart showing the example of the authenticationprocess according to Embodiment 3.

[FIG. 17] is a flowchart showing the example of the authenticationprocess according to Embodiment 3.

[FIG. 18] is a flowchart showing an example of an authentication processaccording to Embodiment 4.

[FIG. 19] is a flowchart showing the example of the authenticationprocess according to Embodiment 4.

[FIG. 20] is a flowchart showing the example of the authenticationprocess according to Embodiment 4.

[FIG. 21] is a flowchart showing the outline of the setup processaccording to Embodiment 1.

[FIG. 22] is a flowchart showing the outline of the biometricinformation registration process according to Embodiment 1.

[FIG. 23] is a flowchart showing the outline of the authenticationprocess according to Embodiment 1.

[FIG. 24] is a flowchart showing the outline of the authenticationprocess according to Embodiment 1.

[FIG. 25] is a diagram showing a hardware configuration of thecertification device, the authentication device, and the decryptiondevice according to Embodiment 1.

DESCRIPTION OF EMBODIMENTS

In the following embodiments, an encryption called Doubly HomomorphicEncryption is employed as the cryptographic system aimed at protectingbiometric information, instead of an ordinary homomorphic encryption.

With the double homomorphic encryption, unlike with the ordinaryhomomorphic encryption, a ciphertext of a combination of sums andproducts on the finite field of original plaintexts can be calculatedfrom a plurality of ciphertexts. For example, a ciphertextE(x₁*y₁+x₂*y₂+ . . . x_(T)*y_(T)) may be calculated by using, forexample, 2T pieces of ciphertexts E(x₁), E(x₂), . . . , E(x_(T)), E(y₁),E(y₂), . . . , and E(y_(T)).

Namely, in the following embodiments, biometric information forregistration is formed of T (T is an integer equal to or larger than 2)pieces of partial data, and biometric information for authentication isformed of T (T is an integer equal to or larger than 2) pieces ofpartial data.

The number of pieces of partial data which have coincident values amongT pieces of partial data registered and T pieces of partial data inputfor authentication, the hamming distance between the T pieces of partialdata registered and T pieces of partial data input for authentication,or the like is derived as a similarity degree. If the similarity degreeis equal to or higher than a predetermined level, the identity of theuser is authenticated.

Examples of the specific algorithm of the doubly homomorphic encryptioninclude algorithms disclosed in Non-Patent Literatures 1 to 3.

To utilize such double homomorphic encryptions in biometricauthentication, a method of generating a feature vector from biometricinformation must be modified, and a method of applying a doublyhomomorphic encryption to a feature vector must be modified.

In biometric authentication, various types of indices are available foridentity checking. Accordingly, various types of methods are availablefor generating a feature vector.

In order to render the feature vector of a plaintext unnecessary in theauthentication process by effectively using the characteristics of thedoubly homomorphic encryption, the index for identity checking needs tobe modified.

The following embodiments disclose: a method for performing identitychecking, using bit strings of 1 and 0 expressing presence and absenceof a feature point, based on the number of positions both having bitvalue of 1; a method for performing identity checking based on thehamming distance between two bit strings; and a method for performingidentity checking based on the Euclidean squared distance betweennumerical value strings.

Also, the encryption application method of each Literature needs to bemodified in accordance with the identity checking method.

In the present invention, Embodiment 1 and Embodiment 2 disclose theapplication method of Non-Patent Literature 1. Embodiment 3 andEmbodiment 4 disclose the application method of Non-Patent Literature 2.

The Okamoto-Takashima encryption algorithm of Non-Patent Literature 1will be explained hereinafter by focusing on a scope necessary forexplaining Embodiment 1 and Embodiment 2.

The Okamoto-Takashima encryption is an encryption that uses bilinearpairing vector spaces defined using an elliptic curve.

A plurality of methods may be available for constituting the bilinearpairing vector spaces. An explanation will be made hereinafter based ona method that constitutes bilinear pairing vector spaces by using adirect product of an elliptic curve.

Generally, an arithmetic operation on a group on an elliptic curve isoften described as an arithmetic operation on an additive group. In thefollowing explanation, however, all arithmetic operations including oneon a finite field will be described as an arithmetic operation on amultiplicative group.

The arithmetic operation will be described according to a more generalscheme that employs asymmetric pairing.

Assume that G, Ĝ, and G_(T) are groups each having a prime order q.

Assume that F_(q)={0, 1, . . . , q−1}. Assume that e:G×Ĝ→G _(T) is apairing that satisfies bilinearity (a property with which e(u^(a),v̂^(b))=e(u, v̂)^(ab) is established for arbitrary u∈G, v̂∈Ĝ, a, b∈F_(q))and non-degenerateness (a property with which g∈G and ĝ∈Ĝ that satisfye(g, ĝ) ≠*1 exist).

Assume that the direct product set of N pieces of groups G is V=G×G× . .. ×G and that the direct product set of N pieces of groups Ĝ is V̂=Ĝ×Ĝ× .. . ×Ĝ.

At this time, the relation indicated by Numerical Expression 4 isestablished.

For

x=(g ^(x1) ,g ^(x2) , . . . , g ^(xN))∈V, y=(g ^(y1),g^(y2) , . . . , g^(yN))∈V, α∈F _(q)  [Numerical Expression 4]

let us define

x+y=(g ^(x1+y1) ,g ^(x2+y2) , . . . , g ^(gN+yN))

and

αx=(g^(αx1),g^(αx2), . . . , g^(αxN))

then, {circumflex over (V)} constitutes a vector space.

Likewise, for

{circumflex over (x)}=(ĝ ^(x1) ,ĝ ^(x2) , . . . , ĝ ^(xN))∈{circumflexover (V)},ŷ=(ĝ ^(y1) ,ĝ ^(y2) , . . . , ĝ ^(yN))∈{circumflex over(V)},α∈F _(q)

let us define

i {circumflex over (x)}+ŷ=(ĝ ^(x1+y1) ,ĝ ^(x2+y2) , . . . , ĝ ^(xN+yN))

and

α{circumflex over (x)}=(ĝ^(αx1),ĝ^(αx2), . . . , ĝ^(αxN))

then, {circumflex over (V)} constitutes a vector space.

Note that in this specification, a symbol formed of a character with “̂”attached above it, such as Ĝ, ĝ, {circumflex over (v)} is the same as asymbol formed of a character with “̂” attached on its side, such as Ĝ, ĝ,or v̂. This applies to Â, Ĉ, â, ĉ, {circumflex over (d)}̂, or ŵ to bedescribed later.

As the pairing of two vector spaces V and V̂, let us define a pairing foru=(u₁, u₂, . . . , u_(N))∈V and v̂=(v̂₁, v̂₂, . . . , v̂_(N))∈V̂as indicatedby Numerical Expression 5.

$\begin{matrix}{{e\left( {u,\hat{v}} \right)} = {\prod\limits_{i = 1}^{N}{e\left( {u_{i},{\hat{v}}_{i}} \right)}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 5} \right\rbrack\end{matrix}$

In the vector spaces V and V̂, a relation indicated by NumericalExpression 6 is established.

Assume that

a₁=(g,1,1, . . . , 1),a₂=(1,g,1, . . . , 1), . . . ,a_(N)=(1,1,1, . . .,g)

and

â₁=(ĝ,1,1, . . . , 1),â₂=(1,ĝ,1), . . . , â_(N)=(1,1,1, . . . , ĝ)

then,

A=(a_(l),a₂, . . . , a_(N)),Â=(â₁,â₂, . . . , â_(N))  [NumericalExpression 6]

are respectively the bases of the vector spaces V and V̂. Also, A and Âsatisfy e(a_(i),â_(j))=e(g,ĝ)^(δ) ^(i,j)where δ_(i,j) is a Kronecker's delta. These bases A and Â will be calledcanonical bases.

Assume that x=x_(i)a₁+x₂a₂+ . . . +x_(N)a_(N)∈V.

Let us define a distortion map φ_(i,j):V→V in the vector space V asφ_(i,j)(x)=x_(j)a_(i).

Likewise, for x̂=x₁â₁+x₂â₂+ . . . +x_(N)â_(N)∈V̂, let us defineφ̂_(i,j):V̂→V̂ as φ̂_(i,j)(x̂)=x_(j)â_(i)

These distortion maps can be calculated easily.

Two vector spaces which have canonical bases and for which a pairing ofthe spaces is defined and a distortion map that can be calculated isdefined, as described above, are called bilinear pairing vector spaces.

Assume that X=(X_(i,j)) and X̂=(X̂_(i,j)) are each an N-row, N-columnsquare matrix whose elements are formed of values selected from F_(q)uniform randomly.

X and X̂ which are constructed in this manner will each become a regularmatrix at a very high probability.

When definition is made as indicated by Numerical Expression 7 by usingsuch regular matrices, then W=(w₁, w₂, . . . , w_(N)) and Ŵ=(ŵ₁, ŵ₂, . .. , ŵ_(N)) also become bases. These bases will be called random bases.

$\begin{matrix}{{w_{i} = {\sum\limits_{j = 1}^{N}{\chi_{i,j}a_{j}}}},{{\hat{w}}_{i} = {\sum\limits_{j = 1}^{N}{{\hat{\chi}}_{i,j}{\hat{a}}_{j}}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 7} \right\rbrack\end{matrix}$

According to Non-Patent Literature 1, concerning random bases W=(w₁, w₂,. . . , w_(N)) and Ŵ=(ŵ₁, ŵ₂, . . . , ŵ_(N)) in the vector spaces V andV̂, the following property is established.

When elements (x₁, x₂, . . . , x_(N)) of F^(N) _(q) are given, it iseasy to obtain x=x₁w₁+x₂w₂+ . . . +x_(N)w_(N) and x̂=x₁ŵ₁+x₂ŵ₂+ . . .+x_(N)ŵ_(N).

However, it is known that when x=x₁w₁+x₂w₂+ . . . +x_(L)w_(L) andx̂=x₁ŵ₁+x₂ŵ₂+ . . . +x_(L)ŵ_(L) (1<L≦N) are given, it is as difficult toobtain vectors y=x₁w₁+x₂w₂+ . . . +x₁w₁ and ŷ=x₁ŵ₁+x₂ŵ₂+ . . . +x₁ŵ₁(1≦1<N) without using X=(X_(i,j)) and X̂=(X̂_(i,j)), as to perform ageneralized Diffie-Hellman calculation.

Meanwhile, if X=(X_(i,j)) and X̂=(X̂_(i,j)) are employed, vectordecomposition as described above can be calculated easily in accordancewith the following algorithm Deco (Numerical Expression 8). Note that kin Numerical Expression 8 is an integer.

$\begin{matrix}{{{{Deco}\left( {x,{< w_{1}},\ldots \mspace{14mu},{w_{l} >},X} \right)}\text{:}}\left. \left( t_{i,j} \right)\leftarrow X^{- 1} \right.\left. y\leftarrow{\sum\limits_{i = 1}^{L}{\sum\limits_{j = 1}^{I}{\sum\limits_{k = 1}^{L}{t_{i,j}x_{j,k}{\varphi_{k,j}(x)}}}}} \right.{{{Deco}\left( {\hat{x},{< {\hat{w}}_{1}},\ldots \mspace{14mu},{{\hat{w}}_{l} >},\hat{X}} \right)}\text{:}}\left. \left( {\hat{t}}_{i,j} \right)\leftarrow{\hat{X}}^{- 1} \right.\left. \hat{y}\leftarrow{\sum\limits_{i = 1}^{L}{\sum\limits_{j = 1}^{I}{\sum\limits_{k = 1}^{L}{{\hat{t}}_{i,j}{\hat{x}}_{j,k}{{\hat{\varphi}}_{k,j}\left( \hat{x} \right)}}}}} \right.} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 8} \right\rbrack\end{matrix}$

From this property, a trapdoor function can be realized by employing aregular matrix as a secret key.

An example of a method of performing biometric authentication by usingbilinear pairing vector spaces, with biometric information being keptencrypted, will be described hereinafter.

EMBODIMENT 1

This embodiment will be exemplified by the following authenticationscheme. An array of feature points is prepared as a feature vector to beused for biometric authentication. If the user has a feature point, 1 isstored in the array; if not, 0 is stored in the array. The resultantarray is treated as the feature vector. In authentication, the number ofpositions where bits 1 coincide is employed as the similarity degreeindex.

To describe in more detail, for example, in the case of fingerprintauthentication, a fingerprint image is divided into small areas, and therunning directions of ridges within the areas are examined. The runningdirections in each area characterize each individual.

Let us assume the following authentication scheme. Four runningdirections (for example, 0°, 45°, 90°, and 135°) are defined for eacharea. The detected running direction is treated as 1, and the otherdirections are treated as 0. Four arrays are prepared for each of all Npieces of areas. The array values are determined according to thedetected values, thus forming a feature vector.

With this authentication scheme, the positions of 1 are almost the samein the feature vectors of one person. Thus, the inner product value ofthe registered feature vector and the feature vector of anauthentication target is expected to be large.

In the feature vector of a different person, the positions of 1 areoften different from those of the person registered. Thus, the innerproduct value of the two feature vectors is expected to be small.

FIG. 1 is a diagram showing a configuration of a biometricauthentication system according to Embodiments 1 to 4.

Referring to FIG. 1, a certification device 101 is a device thatmeasures biometric information of a user and performs a secrecycollation process by using the measured biometric information.

An authentication device 102 is a device that encrypts the biometricinformation of the user, stores the encrypted biometric information, andperforms authentication by using the encrypted biometric informationstored.

A decryption device 103 is a device that decrypts encrypted data.

The certification device 101 is an example of an encryption device, andthe authentication device is an example of a data processing device.

FIG. 2 is a diagram showing an example of the internal configuration ofthe certification device 101.

Referring to FIG. 2, by using various types of sensors such as anoptical camera or infrared camera, a biometric information extractingpart 201 extracts biometric information necessary for personalidentification, from the user.

A feature vector forming part 202 forms a feature vector representingthe feature of the individual from the biometric information extractedby the biometric information extracting part 201.

A random number generating part 203 generates a random number by using apart of a public key.

An encrypting part 204 encrypts the feature vector by using the randomnumber generated by the random number generating part 203.

A storage part 205 stores various types of data such as the public key.The public key stored in the storage part 205 is a public key generatedby the decryption device 103 and distributed by the decryption device103.

A communication part 206 transmits and receives data to and from anotherdevice such as a database.

FIG. 3 is a diagram showing an example of the internal configuration ofthe authentication device 102.

Referring to FIG. 3, a storage part 301 stores various types of datasuch as a feature vector that has been encrypted (to be also referred toas an encrypted feature vector hereinafter), or a public key. Thestorage part 301 is an example of a public key storage part and anencrypted data storage part. Note that the encrypted feature vector tobe stored in the storage part 301 is a feature vector for registrationwhich is encrypted by the certification device 101. A pre-encryptionfeature vector for registration corresponds to an example of first data,and the encrypted feature vector corresponds to an example of encryptedfirst data.

Also, the public key to be stored in the storage part 301 is a publickey generated by the decryption device 103 and distributed by thedecryption device 103.

An encrypted similarity degree generating part 302 calculates encryptedsimilarity degree information from the encrypted feature vectorregistered and the encrypted feature vector for authentication.

The encrypted feature vector for authentication is a feature vector forauthentication which is encrypted by the certification device 101. Apre-encryption feature vector for authentication corresponds to anexample of the second data, and the encrypted feature vector correspondsto an example of encrypted second data.

The encrypted similarity degree information is encrypted informationfrom which the similarity degree between the feature vector forregistration (first data) and the feature vector for authentication(second data) can be derived by the decryption device 103 in accordancewith a decryption process using the secret key that has been generatedto correspond to the public key.

A checking part 303 performs personal identification based on thedecrypted similarity degree and checks whether the user is the correctuser. In other words, the checking part 303 analyzes the similaritydegree and checks whether or not the source of the feature vector forauthentication is correct.

A communication part 304 transmits and receives data to and from thecertification device 101 and the decryption device 103.

More specifically, after the encrypted feature vector for registrationis stored in the storage part 301, the communication part 304 receivesthe encrypted feature vector for authentication from the certificationdevice 101.

The communication part 304 also transmits the encrypted similaritydegree information generated by the encrypted similarity degreegenerating part 302 to the decryption device 103.

The communication part 304 also receives the similarity degree(plaintext) between the feature vector for registration and the featurevector for authentication, which is derived by decrypting, using thesecret key, the encrypted similarity degree information at thedecryption device 103.

The communication part 304 is an example of an encrypted data inputpart, an encrypted similarity degree output part, and a similaritydegree input part.

A random number generating part 305 generates a random number by using apart of the public key.

FIG. 4 is a diagram showing an example of the internal configuration ofthe decryption device 103.

Referring to FIG. 4, a parameter generating part 401 generates aparameter such as a public key or a secret key, which is necessary forencryption and decryption.

A decrypting part 402 decrypts the encrypted similarity degreeinformation to obtain the similarity degree of the plaintext.

A storage part 403 stores various types of data such as the public keyor secret key.

A communication part 404 transmits and receives data to and from anotherdevice such as a database.

A data processing method according to this embodiment will be described.

The overall perspective on the operation will be described first.

The operation is divided into three parts: a setup process, aregistration process, and an authentication process.

In the setup process, the decryption device 103 generates parametersnecessary for encryption and decryption.

In the registration process, the certification device 101 encrypts thebiometric information of the user and sends the encrypted biometricinformation to the authentication device 102. The authentication device102 stores the encrypted biometric information in the storage part 301.

In the authentication process, first, the certification device 101encrypts the biometric information of a user and sends the encryptedbiometric information to the authentication device 102. Then, using theencrypted biometric information of the storage part 301 and theencrypted biometric information received, the authentication device 102generates encrypted similarity degree information and sends it to thedecryption device 103. The decryption device 103 decrypts the similaritydegree and sends the decrypted similarity degree to the authenticationdevice 102. Finally, the authentication device 102 compares thesimilarity degree with the threshold and performs authentication.

The outline of each process will be described hereinafter with referenceto FIGS. 21 to 24.

FIG. 21 shows the outline of the setup process, FIG. 22 shows theoutline of the registration process, and FIGS. 23 and 24 show theoutline of the authentication process.

The outline of the setup process will now be described with reference toFIG. 21.

First, based on the Okamoto-Takashima encryption algorithm, theparameter generating part 401 of the decryption device 103 generates asecret key sk and a public key pk (S2101).

Then, the storage part 403 of the decryption device 103 stores thesecret key sk and the communication part 404 transmits the public key pkto the certification device 101 and the authentication device 102(S2102).

In the certification device 101, the communication part 206 receives thepublic key pk and the storage part 205 stores the public key pk. In theauthentication device 102, the communication part 304 receives thepublic key pk and the storage part 301 stores the public key pk (S2102).

Although an example where the public key pk is transmitted and receivedis described, the public key pk may be distributed to the certificationdevice 101 and the authentication device 102 by another method.

For example, the decryption device 103 may store the public key pk in arecording medium. The certification device 101 and the authenticationdevice 102 may read the public key pk from the recording medium andstore it.

The outline of the registration process will be described with referenceto FIG. 22.

First, in the certification device 101, the biometric informationextracting part 201 extracts the biometric information of the user(S2201).

Then, the feature vector forming part 202 of the certification device101 generates a feature vector b of the biometric information extractedin S2201 (S2202).

Using a part of the public key pk, the random number generating part 203of the certification device 101 generates a random number. Theencrypting part 204 reads the public key pk from the storage part 205.Using the public key pk and the random number, the encrypting part 204encrypts the feature vector b (S2203).

Then, the communication part 206 of the certification device 101transmits an encrypted feature vector C to the authentication device 102(S2204).

The communication part 304 of the authentication device 102 receives theencrypted feature vector C and the storage part 205 stores the encryptedfeature vector C (S2205).

The outline of the authentication process will be described withreference to FIGS. 23 and 24.

First, in the certification device 101, the biometric informationextracting part 201 extracts biometric information of a user (S2301).

Then, the feature vector forming part 202 of the certification device101 generates a feature vector b′ of the biometric information extractedin S2301 (S2302).

Using a part of the public key pk, the random number generating part 203of the certification device 101 generates a random number. Theencrypting part 204 reads the public key pk from the storage part 205.Using the public key pk and the random number, the encrypting part 204encrypts the feature vector b′ (S2303).

The communication part 206 of the certification device 101 transmits anencrypted feature vector Ĉ to the authentication device 102 (S2304).

Then, the communication part 304 of the authentication device 102receives the encrypted feature vector Ĉ (S2305).

Subsequently, the encrypted similarity degree generating part 302 of theauthentication device 102 reads the encrypted feature vector C in thestorage part 301 (S2401).

Using a part of the public key pk, the random number generating part 305of the authentication device 102 generates a random number. Theencrypted similarity degree generating part 302 reads the public key pkfrom the storage part 301. Using the public key pk and the randomnumber, the encrypted similarity degree generating part 302 generatesencrypted similarity degree information for the encrypted feature vectorC read from the storage part 301 and the encrypted feature vector Ĉreceived from the certification device 101 (S2402).

As the authentication device 102 is unable to know the secret key skcorresponding to the public key pk, the authentication device 102 cannotdecrypt the encrypted feature vector C nor the encrypted feature vectorĈ. Thus, encrypted similarity degree information is generated with boththe encrypted feature vector C and encrypted feature vector Ĉ being keptencrypted.

Subsequently, the communication part 304 of the authentication device102 transmits the encrypted similarity degree information to thedecryption device 103 (S2403).

The communication part 404 of the decryption device 103 receives theencrypted similarity degree information (S2404).

Then, the decrypting part 402 of the decryption device 103 reads thesecret key sk from the parameter generating part 401. Using the secretkey sk, the decrypting part 402 performs a decryption process on theencrypted similarity degree information, to derive the similarity degreeof the plaintext (S2405).

The communication part 404 of the decryption device 103 transmits thesimilarity degree of the plaintext to the authentication device 102(S2406). The similarity degree is information that indicates to whatextent the feature vector b for registration and the feature vector b′for authentication are similar to each other. The feature vector and thebiometric information cannot be calculated from the similarity degree.

Then, the communication part 304 of the authentication device 102receives the similarity degree of the plaintext (S2407).

The checking part 303 of the authentication device 102 checks whether ornot the similarity degree of the plaintext is equal to or larger than apredetermined threshold. If the similarity degree of the plaintext isequal to or larger than the threshold, it is determined that the user isthe correct user; if smaller than the threshold, it is determined thatthe user is not the correct user (S2408).

The operations of the respective processes will now be described in moredetail with reference to FIGS. 5 to 9.

FIG. 5 shows the setup process in detail. FIG. 6 shows the registrationprocess in detail. FIGS. 7 to 9 show the authentication process indetail.

The setup will be described with reference to FIG. 5.

In the setup, the decryption device 103 generates the public key pk andthe secret key sk.

The public key pk and the secret key sk may be a public key and a secretkey that are different among users. Alternatively, one public key andone secret key may be provided to one system.

For the sake of explanatory simplicity, a case will be described whereone public key and one secret key are provided to one system. This casecan be easily extended to a case where a different public key and adifferent secret key are provided to a different user.

FIG. 5 is a flowchart showing the procedure of generating the public keypk and the secret key sk in the parameter generating part 401.

First, in step S501, the parameter generating part 401 determines agroup order q, groups G, Ĝ, and G_(T), and generators g∈G and ĝ∈Ĝ.

A practical determining method is described in, for example, Non-PatentLiterature 4, and will accordingly be omitted.

Note that the group order is determined according to the security level,and usually a large-size prime number having, for example, 200 bits or1024 bits is employed as the group order.

In step S502, assuming vector spaces V=G×G×G and V̂=Ĝ×Ĝ×Ĝ, the parametergenerating part 401 determines canonical bases A=(a₁, a₂, a₃) and Â=(â₁,a,̂₂, â₃).

This determining method has previously been described.

In step S503, the parameter generating part 401 takes a value nine timesuniform randomly among integers of 0 to q−1, and by using the obtainedvalues, determines a 3-row 3-column matrix X=(X_(i,j)).

This matrix should be a regular matrix. When a matrix is determined bythis method, the resultant matrix will be a regular matrix at a veryhigh probability. For further accuracy, after determining a matrix inthis manner, the regularity may be checked by, for example, calculatinga determinant. If the matrix is not regular, the elements of the matrixmay be selected again randomly.

In step S504, the parameter generating part 401 takes a value nine timesuniform randomly among integers of 0 to q−1, and by using the obtainedvalues, determines a 3-row 3-column matrix X̂=(X̂_(i,j)).

The obtained matrix will be a regular matrix at a very high probability.If not, the elements of the matrix may be selected again randomly.

In step S505, in accordance with the following Numerical Expressions 9and 10, the parameter generating part 401 determines random bases W=(w₁,w₂, w₃) and Ŵ=(ŵ₁, ŵ₂, ŵ₃).

$\begin{matrix}{w_{i} = {\sum\limits_{j = 1}^{3}{\chi_{i,j}a_{j}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 9} \right\rbrack \\{{\hat{w}}_{i} = {\sum\limits_{j = 1}^{3}{{\hat{\chi}}_{i,j}{\hat{a}}_{j}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 10} \right\rbrack\end{matrix}$

Finally, in step S506, the parameter generating part 401 makes publicthe public key pk=(q, V, V̂, e, G_(T), A, Â, W, Ŵ), and the secret keysk=(X, X̂) is stored in the storage part 403.

A biometric information registration method will be described withreference to FIG. 6.

A case will be described wherein the user registers biometricinformation in the authentication device 102 via the certificationdevice 101. Registration of the biometric information in theauthentication device 102 directly, or via a registration dedicateddevice, can be realized in accordance with the same procedure.

FIG. 6 is a flowchart showing the procedure of registering the biometricinformation in the certification device 101.

First, in step S601, the biometric information extracting part 201extracts the biometric information of the user.

Extraction can be performed by various methods. For example, thebiometric information of the user is extracted by exposing thefingerprint to light and reading its pattern with a sensor.

In step S602, the feature vector forming part 202 forms a feature vectorb=(b₁, b₂, . . . , b_(T)) from the biometric information.

T represents the size of an array that stores the feature vector, and isa value determined depending on the feature-vector forming methods.

According to the forming method of this embodiment, the readout patternis divided into areas, and the presence/absence of a feature point ineach area is detected.

If a feature point is present in an area, 1 is stored at a correspondingposition in the array; if not, 0 is stored at the corresponding positionin the array.

In step S603, the random number generating part 203 takes a value 2Ttimes uniform randomly among integers of 0 to q−1, so that {r_(2,i),r_(3,i)}_(i=1, 2, . . . , T) is obtained.

Note that q in q−1 is q included in the public key pk.

In step S604, using c_(i)=b_(i)w₁+r_(2,i)w₂+r_(3,i)w₃, the encryptingpart 204 calculates the encrypted feature vector C=(c₁, c₂, . . . ,c_(T)).

Note that w₁, w₂, and w₃ have been distributed by the decryption device103 as a part (W) of the public key.

In step S605, the communication part 206 transmits the encrypted featurevector C=(c₁, c₂, . . . , C_(T)) to the authentication device 102.

In the transmission, a communication manipulation detection techniquesuch as SSL (Secure Sockets Layer) may be desirably employed somanipulation will not be conducted during communication.

Finally, in step S606, the communication part 304 in the authenticationdevice 102 receives the encrypted feature vector C=(c₁, c₂, . . . ,C_(T)) and stores it in the storage part 301.

The authentication method will be described with reference to FIGS. 7 to9.

For the sake of simplicity, a case of so-called 1:1 authentication willbe described where, in the authentication, the user as theauthentication target is separately specified by ID information or thelike.

FIGS. 7, 8, and 9 are flowcharts showing the procedure ofauthentication.

First, in step S701, the biometric information extracting part 201 ofthe certification device 101 extracts the biometric information of theuser.

The extracting method is the same as that employed in the biometricinformation registration.

In step S702, the feature vector forming part 202 of the certificationdevice 101 forms a feature vector b′=(b′₁, b′₂, . . . , b′_(T)) from thebiometric information.

The forming method is the same as that employed for biometricinformation registration.

In step S703, the random number generating part 203 of the certificationdevice 101 takes a value 2T times uniform randomly among integers of 0to q−1 to obtain {r′_(2,i)r′_(3,i)}_(i=1, 2, . . . , T).

In step S704, using ĉ_(i)=(b′_(i)ŵ₁+r′_(2,i)ŵ₂+r′_(3,i)ŵ₃), theencrypting part 204 of the certification device 101 calculates theencrypted feature vector Ĉ=(ĉ₁, ĉ₂, . . . , ĉ_(T)).

Note that ŵ₁, ŵ₂, and ŵ₃ have been distributed by the decryption device103 as a part (Ŵ) of the public key.

In step S705, the communication part 206 of the certification device 101transmits the encrypted feature vector Ĉ=(ĉ₁, ĉ₂, . . . , ĉ_(T)) to theauthentication device 102.

In the transmission, a communication manipulation detection techniquesuch as SSL may be desirably employed so manipulation will not beconducted during communication.

In step S706, the communication part 304 in the authentication device102 receives the encrypted feature vector Ĉ=(ĉ₁, ĉ₂, . . . , ĉ_(T)).

In step S707, the encrypted similarity degree generating part 302 in theauthentication device 102 takes the encrypted feature vector C=(c₁, c₂,. . . , c_(T)) from the storage part 301.

In general, encrypted biometric information of a large number of usersare stored in the storage part 301, and which information to take isdetermined using separately provided ID information.

In step S708, the random number generating part 305 of theauthentication device 102 takes a value 6T times uniform randomly amongintegers of 0 to q−1 to obtain {s_(1,i), s_(2,i), s_(3,i), ŝ_(1,i),ŝ_(2,i), ŝ_(3,i)}_(i=1, 2, . . . , T).

In step S709, the random number generating part 305 of theauthentication device 102 takes a value 4 times uniform randomly amongintegers of 0 to q−1 to obtain {u₂, u₃, û₂, û₃}.

In step S710, the encrypted similarity degree generating part 302 of theauthentication device 102 calculatesd_(i)=c_(i)+s_(1,i)w₁+s_(2,i)w₂+s_(3,i)w₃.

The encrypted similarity degree generating part 302 performs thiscalculation for every i=1, 2, . . . , T.

Note that w₁, w₂, and w₃ have been distributed by the decryption device103 as a part (W) of the public key.

In step S711, the encrypted similarity degree generating part 302 of theauthentication device 102 calculatesd̂_(i)=ĉ_(i)+ŝ_(1,i)ŵ₁+ŝ_(2,i)ŵ₂+ŝ_(3,i)ŵ₃.

The encrypted similarity degree generating part 302 performs thiscalculation for every i=1, 2, . . . , T.

Note that ŵ₁, ŵ₂, and ŵ₃ have been distributed by the decryption device103 as a part (Ŵ) of the public key.

In step S712, the encrypted similarity degree generating part 302 of theauthentication device 102 calculates E in accordance with NumericalExpression 11.

$\begin{matrix}{E = {{\sum\limits_{i = 1}^{T}\left( {{{\hat{s}}_{1,i}c_{i}} + {s_{1,i}{\hat{s}}_{1,i}w_{1}}} \right)} + {u_{2}w_{2}} + {u_{3}w_{3}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 11} \right\rbrack\end{matrix}$

In step S713, the encrypted similarity degree generating part 302 of theauthentication device 102 calculates Ê in accordance with NumericalExpression 12.

$\begin{matrix}{\hat{E} = {{\sum\limits_{i = 1}^{T}{s_{1,i}{\hat{c}}_{i}}} + {{\hat{u}}_{2}{\hat{b}}_{2}} + {{\hat{u}}_{3}{\hat{b}}_{3}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 12} \right\rbrack\end{matrix}$

In step S714, the communication part 304 of the authentication device102 transmits (d₁, . . . , d_(T), d̂₁, . . . , d̂_(T), E, Ê) to thedecryption device 103.

In the transmission, a communication manipulation detection techniquesuch as SSL may be desirably employed so manipulation will not beconducted during communication.

Note that (d₁, . . . d_(T), d̂₁, . . . , d̂_(T), E, Ê) described abovecollectively constitutes the encrypted similarity degree information.

In step S715, the communication part 404 of the decryption device 103receives (d₁, . . . , d_(T), d̂_(I), . . . , d̂_(T), E, Ê).

In step S716, the decrypting part 402 of the decryption device 103 takesthe secret key sk=(X, X̂) from the storage part 403.

In step S717, the decrypting part 402 of the decryption device 103calculates an inverse matrix X⁻¹=(t_(i,j)) of X and an inverse matrixX̂⁻¹=(t̂_(i,j)) of X̂.

Instead of calculating these values each time, calculated values may bestored in the storage part 403 in advance and taken out.

In step S718, the decryption device 103 calculates Z₁ in accordance withNumerical Expression 13.

$\begin{matrix}{Z_{1} = {\prod\limits_{i = 1}^{T}{e\left( {{{Deco}\left( {d_{i},{\langle w_{1}\rangle},X} \right)},{{Deco}\left( {{\hat{d}}_{i},{\langle{\hat{w}}_{1}\rangle},\hat{X}} \right)}} \right)}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 13} \right\rbrack\end{matrix}$

The Deco algorithm is calculated in accordance with the followingNumerical Expression 14. Note that k in Numerical Expression 14 is aninteger.

$\begin{matrix}{{{{Deco}\left( {d_{i},{< w_{1} >},X} \right)}\text{:}}{y = {\sum\limits_{i = 1}^{3}{\sum\limits_{k = 1}^{3}{t_{i,1}x_{1,k}{\varphi_{k,i}\left( d_{i} \right)}}}}}{{{Deco}\left( {{\hat{d}}_{i},{< {\hat{w}}_{1} >},\hat{X}} \right)}\text{:}}{\hat{y} = {\sum\limits_{i = 1}^{3}{\sum\limits_{k = 1}^{3}{{\hat{t}}_{i,1}{\hat{x}}_{1,k}{\varphi_{k,i}\left( {\hat{d}}_{i} \right)}}}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{11mu} 14} \right\rbrack\end{matrix}$

In step S719, the decrypting part 402 of the decryption device 103calculates Z₂=e(Deco(E, <w₁>, X), ŵ₁)·e(w₁, Deco(Ê, <ŵ₁>, X̂)).

This Deco algorithm is calculated in the same manner as described above.

In step S720, the decrypting part 402 of the decryption device 103calculates Z=Z₁/Z₂.

In step S721, the decrypting part 402 of the decryption device 103calculates a discrete logarithm d of Z having a base e(g, ĝ).

This discrete logarithm d corresponds to the number of coincidences offeature points and represents the similarity degree.

Calculation of a discrete logarithm is regarded difficult for thecurrent computer performance. A small d, however, can be calculatedefficiently.

In this embodiment, since d is sufficiently smaller as compared to theorder q, it can be calculated efficiently.

In step S722, the communication part 404 of the decryption device 103transmits the similarity degree d to the authentication device 102.

In the transmission, a communication manipulation detection techniquesuch as SSL may be desirably employed so manipulation will not beconducted during communication.

In step S723, the communication part 304 of the authentication device102 receives the similarity degree d.

In step S724, whether or not the similarity degree d is equal to orlarger than the threshold is checked.

The threshold is a value determined by the system in advance by takinginto account various factors such as the type of biometric informationto be utilized or the security requirements.

If the similarity degree d is equal to or larger than the threshold, itis determined that the encrypted biometric information sent from thecertification device 101 belongs to the correct user specified by theID.

If the similarity degree d is less than the threshold, it is determinedthat the encrypted biometric information sent from the certificationdevice 101 does not belong to the correct user specified by the ID butbelongs to a different person.

Through the above steps, the authentication device 102 can performbiometric authentication with the certification device 101.

According to the above embodiment, the feature vector is not stored inthe authentication device 102 as it is, but is stored in an encryptedstate. This can decrease the risk for the user that the feature vectorwhich is privacy information might be secretly read by the administratorof the authentication device 102.

On the side of the authentication device 102, even if the encryptedfeature vector should leak, the original feature vector itself will notleak. Thus, the data administration work can be reduced as compared to acase where the feature vector itself is stored.

According to the procedure of this embodiment, the decryption device 103can decrypt only the similarity degree which is an index, and cannotdecrypt the feature vector.

Unless the certification device 101 and decryption device 103 worktogether, the feature vector will not be exposed in the authenticationprocess. Therefore, biometric authentication with the biometricinformation being kept secret is possible.

According to this embodiment, in authentication, once the certificationdevice 101 sends an encrypted feature vector to the authenticationdevice 102, the authentication process can be conducted between theauthentication device 102 and the decryption device 103. In 1:Nauthentication particularly, communication need not be performed betweenthe certification device 101 and the authentication device 102 thenumber of times proportional to the number of users. As a result, thecommunication amount can be decreased.

Also, according to this embodiment, in authentication, once thecertification device 101 sends an encrypted feature vector to theauthentication device 102, the authentication process can be conductedbetween the authentication device 102 and the decryption device 103.Hence, the biometric information acquired in the certification device101 can be deleted immediately.

As a result, the risk of biometric information theft in thecertification device 101 can be diminished.

In this embodiment, in constructing the feature vector, 1 is stored at aposition where a feature point is present, and 0 is stored at a positionwhere a feature point is not present. The inner product is calculatedusing vectors each constituted of 1 and 0. The concept of significancemay be introduced additionally, and a significant feature point may beweighted (for example, 5 is stored in place of 1).

With this structure, when compared to a case where simply the innerproduct is calculated, biometric authentication that is more precise canbe realized.

In this embodiment, a method using three-dimensional dual pairing vectorspaces is disclosed. Three-dimensional is merely an example, and thevector space need not always be three-dimensional.

The present invention can be practiced with, for example, atwo-dimensional vector space, a four-dimensional vector space, or afurther higher-dimensional vector space.

In the case of a two-dimensional vector space, the present invention maybe practiced by removing vectors w₃ and ŵ₃ appearing in the aboveembodiment.

This can reduce the calculation amount in the registration andauthentication of the biometric information.

In the case of a four-dimensional vector space or a furtherhigher-dimensional vector space, the additional vectors may serve thesame roles of w₂, w₃, ŵ₂, and ŵ₃.

More specifically, when calculating c_(i), ĉ_(i), d_(i), and d̂_(i), theadditional vectors may be multiplied by a random-number factor andsummed with w₂, w₃, ŵ₂, and ŵ₃, respectively.

Then, a ciphertext that is more difficult to decipher can be formed,thus improving the security.

In this embodiment, for improving the security, in authentication, {u₂,u₃, û₂, û₃} is selected in step S709 and is used in step S712 and stepS713. Alternatively, these steps can be omitted.

This eliminates the procedure of authentication, thus reducing thecalculation amount.

EMBODIMENT 2

Embodiment 1 described above discloses the authentication method whereinbiometric authentication is performed using the number of coincidencesof feature points as the performance index. An authentication methodwill now be described below wherein biometric authentication isperformed using the hamming distance or Euclidean squared distancebetween the feature vectors.

A configuration example of a biometric authentication system accordingto this embodiment is the same as that shown in FIG. 1.

The examples of the internal configurations of the certification device101, authentication device 102, and decryption device 103 according tothis embodiment are the same as those shown in FIGS. 2 to 4.

According to this embodiment, T pieces of arrays are prepared in thesame manner as in Embodiment 1, thus constituting a feature vector. Asthe similarity degree index, the hamming distance or Euclidean squareddistance between two feature vectors is employed. Assume that the twofeature vectors are b=(b₁, b₂, . . . , b_(T)) and b′=(b′₁, b′₂, . . . ,b′_(T)).

The hamming distance between the two feature vectors is given byNumerical Expression 15 (note that b′_(i), b′_(i)∈{0, 1}), and theEuclidean squared distance between two feature vectors is given byNumerical Expression 16.

$\begin{matrix}{{d_{H}\left( {b,b^{\prime}} \right)} = {{\sum\limits_{i = 1}^{T}\left( {b_{i} \oplus b_{i}^{\prime}} \right)} = {\sum\limits_{i = 1}^{T}\left( {b_{i} - b_{i}^{\prime}} \right)^{2}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 15} \right\rbrack \\{\mspace{79mu} {{d_{E\; 2}\left( {b,b^{\prime}} \right)} = {\sum\limits_{i = 1}^{T}{\left( {b_{i} - b_{i}^{\prime}} \right)^{2}.}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 16} \right\rbrack\end{matrix}$

A parameter generating method according to this embodiment is the sameas that shown in FIG. 5 of Embodiment 1, and a description thereof willaccordingly be omitted.

A biometric information registration method will be described withreference to FIG. 10.

A case will be described wherein the user registers biometricinformation in the authentication device 102 via the certificationdevice 101. Registration of the biometric information in theauthentication device 102 directly, or via a registration dedicateddevice, can be realized in accordance with the same procedure.

FIG. 10 is a flowchart showing the procedure of registering thebiometric information in the certification device 101.

Step S1001 and step S1002 are the same as their counterparts inEmbodiment 1.

Note that with the hamming distance, b_(i)∈{0, 1} is satisfied, and withthe Euclidean squared distance, b_(i)∈{0, 1, . . . , q−1} is satisfied.

Then, in step S1003, the random number generating part 203 takes a value4T times uniform randomly among integers of 0 to q−1, so that {r_(2,i),r^(3,i), r̂_(2,i), r̂_(3,i)}_(i=1, 2, . . . , T) is obtained.

In step S1004, using c_(i)=b_(i)w₁+r_(2,i)w₂+r_(3,i)w₃ andĉ_(i)=b_(i)ŵ₁+r̂_(2,i)ŵ₂+̂_(3,i)ŵ₃, the encrypting part 204 calculates theencrypted feature vectors C=(c₁, c₂, . . . , c_(T)) and Ĉ=(ĉ₁, ĉ₂, . . ., ĉ_(T)).

Note that w₁, w₂, and w₃ and ŵ₁, ŵ₂, and ŵ₃ have been distributed by thedecryption device 103 as parts (W and Ŵ) of the public key.

In step S1005, the communication part 206 transmits the encryptedfeature vectors C=(c₁, c₂, . . . , c_(T)) and Ĉ=(ĉ₁, ĉ₂, . . . , ĉ_(T))to the authentication device 102.

In the transmission, a communication manipulation detection techniquesuch as SSL may be desirably employed so manipulation will not beconducted during communication.

Finally, in step S1006, the authentication device 102 stores theencrypted feature vectors C=(c₁, c₂, . . . , c_(T)) and Ĉ=(ĉ₁, ĉ₂, . . ., ĉ_(T)) and stores them in the storage part 301.

The authentication method will be described with reference to FIGS. 11,12, and 13.

For the sake of simplicity, a case of so-called 1:1 authentication willbe described where, in the authentication, the user as theauthentication target is separately specified by ID information or thelike.

Step S1101 and step S1102 are the same as their counterparts inEmbodiment 1.

Note that with the hamming distance, b′_(i)∈{0, 1} is satisfied, andwith the Euclidean squared distance, b′_(i)∈{0, 1, . . . , q−1} issatisfied.

In step S1103, the random number generating part 203 of thecertification device 101 takes a value 4T times uniform randomly amongintegers of 0 to q−1 to obtain {r′_(2,i), r′_(3,i), r̂′_(2,i),r̂′_(3,i)}_(i=1, 2, . . . , T).

In step S1104, using c′_(i)=b′_(i)w₁+r′_(2,i)w₂+r′_(3,i)w₃ andĉ_(i)=b′_(i)ŵ₁+r′_(2,i)ŵ₂+r′_(3,i)ŵ₃, the encrypting part 204 of thecertification device 101 calculates the encrypted feature vectorsC′=(c′₁, c′₂, . . . , c′_(T)) and Ĉ′=(ĉ′₁, ĉ′₂, . . . , ĉ′_(T)).

In step S1105, the communication part 206 of the certification device101 transmits the encrypted feature vectors C′=(c′₁, c′₂, . . . ,c′_(T)) and Ĉ′=(ĉ′₁, ĉ′₂, . . . , ĉ′_(T)) to the authentication device102.

In the transmission, a communication manipulation detection techniquesuch as SSL may be desirably employed so manipulation will not beconducted during communication.

In step S1106, the communication part 206 in the authentication device102 receives the encrypted feature vectors C′=(c′₁, c′₂, . . . , c′_(T))and Ĉ′=(ĉ′₁, ĉ′₂, . . . , ĉ′_(T)).

In step S1107, the encrypted similarity degree generating part 302 inthe authentication device 102 takes the encrypted feature vectors C=(c₁,c₂, . . . , c_(T)) and Ĉ=(ĉ₁, ĉ₂, . . . , ĉ_(T)) from the storage part301.

In general, encrypted biometric information of a large number of usersare stored in the storage part 301, and which information to take isdetermined using separately provided ID information.

In step S1108, the random number generating part 203 of theauthentication device 102 takes a value 6T times uniform randomly amongintegers of 0 to q−1 to obtain {s_(1,i), s_(2,i), s_(3,i), ŝ_(1,i),ŝ_(2,i), ŝ_(3,i)}_(i=1, 2, . . . , T).

In step S1109, the random number generating part 203 of theauthentication device 102 takes a value 4 times uniform randomly amongintegers of 0 to q−1 to obtain {u₂, u₃, û₂, û₃}.

In step S1110, the encrypted similarity degree generating part 302 ofthe authentication device 102 calculatesd_(i)=(c_(i)−c′_(i))+s_(1,i)w₁+s_(2,i)w₂+s_(3,i)w₃.

Note that w₁, w₂, and w₃ have been distributed by the decryption device103 as a part (W) of the public key.

In step S1111, the encrypted similarity degree generating part 302 ofthe authentication device 102 calculatesd̂_(i)=(ĉ_(i)−ĉ′_(i))+ŝ_(1,i)ŵ₁+ŝ_(2,i)ŵ₂+ŝ_(3,i)ŵ₃.

Note that ŵ₁, ŵ₂, and ŵ₃ have been distributed by the decryption device103 as a part (Ŵ) of the public key.

In step S1112, the encrypted similarity degree generating part 302 ofthe authentication device 102 calculates E in accordance with NumericalExpression 17.

$\begin{matrix}{E = {{\sum\limits_{i = 1}^{T}\left( {{{\hat{s}}_{1,i}\left( {c_{i} - c_{i}^{\prime}} \right)} + {s_{1,i}{\hat{s}}_{1,i}w_{1}}} \right)} + {u_{2}w_{2}} + {u_{3}w_{3}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 17} \right\rbrack\end{matrix}$

In step S1113, the encrypted similarity degree generating part 302 ofthe authentication device 102 calculates Ê in accordance with NumericalExpression 18.

$\begin{matrix}{\hat{E} = {{\sum\limits_{i = 1}^{T}{s_{1,i}\left( {{\hat{c}}_{i} - {\hat{c}}_{i}^{\prime}} \right)}} + {{\hat{u}}_{2}{\hat{w}}_{2}} + {{\hat{u}}_{3}{\hat{w}}_{3}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 18} \right\rbrack\end{matrix}$

In step S1114, the communication part 206 of the authentication device102 transmits (d₁, . . . , d_(T), d̂₁, . . . , d̂_(T) . . . , E, Ê) to thedecryption device 103.

In the transmission, a communication manipulation detection techniquesuch as SSL may be desirably employed so manipulation will not beconducted during communication.

Note that in this embodiment, (d₁, . . . , d_(T), d̂₁, . . . , d̂_(T) . .. , E, Ê) is an example of the encrypted similarity degree information.

Steps subsequent to this step are the same as those of Embodiment 1, anda description thereof will accordingly be omitted.

According to the above embodiment, the same effect as that of Embodiment1 can be obtained. Also, the hamming distance or Euclidean squareddistance can be used as the similarity degree index.

EMBODIMENT 3

Embodiments 1 and 2 described above disclose the methods whereinbiometric authentication is performed using the Okamoto-Takashimaencryption. An authentication method will be described below whereinbiometric authentication is performed using a BGN (Boneh-Goh-Nissim)encryption indicated in Non-Patent Literature 2.

A configuration of a biometric authentication system according to thisembodiment is also the same as that shown in FIG. 1.

The examples of the internal configurations of the certification device101, authentication device 102, and decryption device 103 according tothis embodiment are also the same as those shown in FIGS. 2 to 4.

First, the BGN encryption algorithm will be described.

A BGN encryption consists of three algorithms: key generation,encryption, and decryption.

The key generation algorithm is as follows.

Assume that p and q are respectively prime numbers.

Groups G and G_(T) each having an order N are generated where N=pq.

Assume that e:G×G→G_(T) is a pairing that satisfies bilinearity andnon-degenerateness.

Assume that g and u are elements selected from G uniform randomly.

Using h=u^(q), h is determined.

Assume that the public key is ((G, G_(T), N, e), g, h) and that thesecret key is p.

The encryption algorithm is as follows.

Assume that the plaintext space is {0, 1, . . . , L}. Among {0, 1, . . ., N−1}, r is selected uniform randomly.

Assume that a ciphertext E(x) corresponding to x is E(x)=g^(x)h^(r).

The decryption algorithm is as follows.

Assuming that the ciphertext is E(x), first, using the secret key p,E(x)^(P) is calculated.

From the definition, E(x)^(P)=((g^(x)h^(r))^(P)=(g^(P))^(x).

Concerning this value, a discrete logarithm having a base g^(P) iscalculated, so that the original plaintext x is obtained.

Calculation of a discrete logarithm is regarded difficult for thecurrent computer performance. It is, however, known that if theplaintext space L has a small size, using Pollard's Lambda Method, thediscrete logarithm can be calculated with a calculation amount of assmall as √L.

A method of performing biometric authentication using such a BGNencryption will now be described.

In this embodiment, description will be made on a case where the samefeature vector constituting method as that of Embodiment 1 is employed.

More specifically, this embodiment will be exemplified by the followingauthentication scheme. An array of feature points is prepared as afeature vector to be used for biometric authentication. If the user hasa feature point, 1 is stored in the array; if not, 0 is stored in thearray. The resultant array is treated as the feature vector. Inauthentication, the number of positions where bits 1 coincide isemployed as the similarity degree index.

The setup will be described with reference to FIG. 13.

FIG. 13 is a flowchart showing the procedure of generating the publickey and the secret key in the parameter generating part 401.

First, in step S1301, the parameter generating part 401 determines primenumbers p and q and groups G and G_(T).

Note that the prime number is determined according to the securitylevel. As the product of prime numbers p and q is used as the grouporder, usually a large-size prime number having, for example, 200 bitsor 1024 bits is employed.

In step S1302, the parameter generating part 401 selects g and u uniformrandomly from G, and calculates h=u^(q).

Finally, in step S1303, the parameter generating part 401 makes publicthe public key pk=((G, G_(T), N, e), g, h), and the secret key sk=p isstored in the storage part 403.

A biometric information registration method will be described withreference to FIG. 14.

A case will be described wherein the user registers biometricinformation in the authentication device 102 via the certificationdevice 101. Registration of the biometric information in theauthentication device 102 directly, or via a registration dedicateddevice, can be realized in accordance with the same procedure.

FIG. 14 is a flowchart showing the procedure of registering thebiometric information in the certification device 101.

First, in step S1401, the biometric information extracting part 201extracts the biometric information of the user. Extraction can beperformed by various methods. For example, the biometric information ofthe user is extracted by exposing the fingerprint to light and readingits pattern with a sensor.

In step S1402, the feature vector forming part 202 forms a featurevector b=(b₁, b₂, . . . , b_(T)) from the biometric information.

In step S1403, the random number generating part 203 takes a value Ttimes uniform randomly among integers of 0 to N−1, so that{r_(i)}_(i=1, 2, . . . , T) is obtained.

In step S1404, using c_(i)=g^(bi)h^(ri), the encrypting part 204calculates the encrypted feature vector C=(c₁, c₂, . . . , c_(T)).

Note that g and h have been distributed by the decryption device 103 asa part (W) of the public key.

In step S1405, the communication part 206 transmits the encryptedfeature vector C=(c₁, c₂, . . . , c_(T)) to the authentication device102.

Finally, in step S1406, the authentication device 102 stores theencrypted feature vector C=(c₁, c₂, . . . , c_(T)) in the storage part301.

The authentication method will be described with reference to FIGS. 15to 17.

For the sake of simplicity, a case of so-called 1:1 authentication willbe described where, in the authentication, the user as theauthentication target is separately specified by ID information or thelike.

FIGS. 15, 16, and 17 are flowcharts showing the procedure ofauthentication.

First, in step S1501, the biometric information extracting part 201 ofthe certification device 101 extracts the biometric information of theuser.

The extracting method is the same as that employed in the biometricinformation registration.

In step S1502, the feature vector forming part 202 of the certificationdevice 101 forms a feature vector b′=(b′₁, b′₂, . . . , b′_(T)) from thebiometric information.

The forming method is the same as that employed for biometricinformation registration.

In step S1503, the random number generating part 203 of thecertification device 101 takes a value T times uniform randomly amongintegers of 0 to N−1 to obtain {r′_(i)}_(i=1, 2, . . . , T).

In step S1504, using c′_(i)=g^(b′i)h^(r′i), the encrypting part 204 ofthe certification device 101 calculates the encrypted feature vectorC′=(c′₁, c′₂, . . . , c′_(T)).

In step S1505, the communication part 206 of the certification device101 transmits the encrypted feature vector C′=(c′₁, c′₂, . . . , c′_(T))to the authentication device 102.

In the transmission, a communication manipulation detection techniquesuch as SSL may be desirably employed so manipulation will not beconducted during communication.

In step S1506, the communication part 206 in the authentication device102 receives the encrypted feature vector C′=(c′₁, c′₂, . . . , c′_(T)).

In step S1507, the encrypted similarity degree generating part 302 inthe authentication device 102 takes the encrypted feature vector C=(c₁,c₂, . . . , c_(T)) from the storage part 301.

In step S1508, the random number generating part 305 of theauthentication device 102 takes a value uniform randomly among integersof 0 to N−1 to obtain s.

In step S1509, the encrypted similarity degree generating part 302 ofthe authentication device 102 calculates E in accordance with NumericalExpression 19.

$\begin{matrix}{E = {\sum\limits_{i = 1}^{T}{{e\left( {c_{i},c_{i}^{\prime}} \right)} \cdot {e\left( {g,h} \right)}^{s}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 19} \right\rbrack\end{matrix}$

In step S1510, the communication part 304 of the authentication device102 transmits E to the decryption device 103.

In the transmission, a communication manipulation detection techniquesuch as SSL may be desirably employed so manipulation will not beconducted during communication.

In this embodiment, E serves as the encrypted similarity degreeinformation.

In step S1511, the communication part 404 of the decryption device 103receives E.

In step S1512, the decrypting part 402 of the decryption device 103takes the secret key p from the storage part 403.

In step S1513, the decrypting part 402 of the decryption device 103calculates Z=E^(P).

In step S1514, the decrypting part 402 of the decryption device 103calculates a discrete logarithm d of Z having a base e(g, g)^(P).

This discrete logarithm d corresponds to the similarity degree in thisembodiment as well.

In step S1515, the communication part 404 of the decryption device 103transmits d to the authentication device 102. In the transmission, acommunication manipulation detection technique such as SSL may bedesirably employed so manipulation will not be conducted duringcommunication.

In step S1516, the communication part 304 of the authentication device102 receives the similarity degree d.

In step S1517, the checking part 303 checks whether or not thesimilarity degree is equal to or larger than the threshold.

The threshold is a value determined by the system in advance by takinginto account various factors such as the type of biometric informationto be utilized or the security requirements.

If the similarity degree d is equal to or larger than the threshold, itis determined that the encrypted biometric information sent from thecertification device 101 belongs to the correct user specified by theID.

If the similarity degree d is less than the threshold, it is determinedthat the encrypted biometric information sent from the certificationdevice 101 does not belong to the correct user specified by the ID butbelongs to a different person.

Through the above steps, the authentication device 102 can performbiometric authentication with the certification device 101.

According to the above embodiment, the same effect as that of Embodiment1 can be obtained. Also, the number of public keys and the number ofsecret keys can be smaller than in Embodiment 1.

Also, as compared to Embodiment 1, the number of ciphertexts to be sentto the decryption device 103 can be decreased.

EMBODIMENT 4

Embodiment 3 described above discloses the authentication method whereinthe inner product of feature vectors is calculated and biometricauthentication is performed using the obtained value. An authenticationmethod will now be described below wherein biometric authentication isperformed using the hamming distance or Euclidean squared distancebetween the feature vectors.

A configuration example of a biometric authentication system accordingto this embodiment is the same as that shown in FIG. 1. The examples ofthe internal configurations of the certification device 101,authentication device 102, and decryption device 103 according to thisembodiment are the same as those shown in FIGS. 2 to 4.

A parameter generating method and a biometric information registrationmethod according to this embodiment are the same as those of Embodiment3, and a description thereof will accordingly be omitted.

The authentication method will be described with reference to FIGS. 18,19, and 20.

For the sake of simplicity, a case of so-called 1:1 authentication willbe described where, in the authentication, the user as theauthentication target is separately specified by ID information or thelike.

Steps S1801 through S1808 are the same as their counterparts inEmbodiment 3, and a description thereof will accordingly be omitted.

In step S1809, the encrypted similarity degree generating part 302 ofthe authentication device 102 calculates E in accordance with NumericalExpression 20.

$\begin{matrix}{E = {\sum\limits_{i = 1}^{T}{{e\left( {c_{i},g} \right)} \cdot {e\left( {c_{i}^{\prime},g} \right)} \cdot {e\left( {c_{i},c_{i}^{\prime}} \right)}^{- 2} \cdot {e\left( {g,h} \right)}^{s}}}} & \left\lbrack {{Numerical}\mspace{14mu} {Expression}\mspace{14mu} 20} \right\rbrack\end{matrix}$

Steps subsequent to this step are the same as those of Embodiment 3, anda description thereof will accordingly be omitted.

According to the above embodiment, in addition to the same effect asthat of Embodiment 2, the same effect as that of Embodiment 3 can alsobe obtained.

So far the biometric authentication methods using a doubly homomorphicencryption are disclosed in Embodiments 1 to 4. It is obvious thatapplication of the biometric authentication is not limited to biometricauthentication but includes a pattern matching field as well.

More specifically, according to the authentication methods indicated inEmbodiments 1 to 4, the similarity degree of data can be checked withthe data being kept encrypted.

As a result, image search, video search, voice search, and the likebecome possible with the data being kept encrypted.

The above Embodiments 1 to 4 indicate that, using biometricauthentication and the doubly homomorphic encryption, biometricauthentication is realized with the biometric information being keptencrypted.

More specifically, conventionally, since an ordinary homomorphicencryption is employed, the authentication process cannot be performedwith every information being kept encrypted. This leads to a problemthat in the authentication process, the communication amount between theuser and the authentication device may undesirably increase.

By employing the doubly homomorphic encryption, the authenticationprocess can be performed with every information being kept encrypted.This leads to an effect that the communication amount between the userand the authentication device can be decreased.

The combination of biometric authentication and doubly homomorphicencryption realizes biometric authentication that is secure and has highcommunication amount efficiency.

Finally, a hardware configuration example of each of the certificationdevice 101, authentication device 102, and decryption device 103 shownin Embodiments 1 to 4 will be described.

FIG. 25 shows an example of the hardware resource of each of thecertification device 101, authentication device 102, and decryptiondevice 103 shown in

Embodiments 1 to 4.

Note that the configuration of FIG. 25 is merely an example of thehardware configuration of the certification device 101, authenticationdevice 102, and decryption device 103. The hardware configuration of thecertification device 101, authentication device 102, and decryptiondevice 103 is not limited to that shown in FIG. 25, but anotherconfiguration may be possible.

Referring to FIG. 25, each of the certification device 101,authentication device 102, and decryption device 103 includes a CPU 911(also referred to as a Central Processing Unit, central processingdevice, processing device, computation device, microprocessor,microcomputer, or processor) that executes programs.

The CPU 911 is connected to, for example, a ROM (Read Only Memory) 913,a RAM (Random Access Memory) 914, a communication board 915, a displaydevice 901, a keyboard 902, a mouse 903, and a magnetic disk device 920via a bus 912, and controls these hardware devices. Furthermore, the CPU911 may be connected to an FDD 904 (Flexible Disk Drive), a compact diskdevice 905 (CDD), or a printer device 906. The certification device 101is connected to a read device 907 which reads biometric information. Inplace of the magnetic disk device 920, a storage device such as anoptical disk device or memory card (registered trademark) read/writedevice may be employed.

The RAM 914 is an example of a volatile memory. The storage media,namely the ROM 913, FDD 904, CDD 905, and magnetic disk device 920, areexamples of a nonvolatile memory. These devices are examples of thestorage device.

The “storage part” described in Embodiments 1 to 4 is realized by theRAM 914, magnetic disk device 920, or the like.

The communication board 915, keyboard 902, mouse 903, read device 907,FDD 904, and the like are examples of an input device.

The communication board 915, display device 901, printer device 906, andthe like are examples of an output device.

The communication board 915 may be connected to, for example, a LAN(Local Area Network), the Internet, a WAN (Wide Area Network), or a SAN(Storage Area Network) as well, in addition to other devices.

The magnetic disk device 920 stores an operating system 921 (OS), awindow system 922, programs 923, and files 924.

The CPU 911 executes each program of the programs 923 by utilizing theoperating system 921 and the window system 922.

The RAM 914 temporarily stores at least some programs of the operatingsystem 921 and application programs that are executed by the CPU 911.

The RAM 914 also stores various types of data necessary for the processperformed by the CPU 911.

The ROM 913 stores the BIOS (Basic Input Output System) program. Themagnetic disk device 920 stores the boot program.

When the certification device 101, the authentication device 102, or thedecryption device 103 is booted, the BIOS program of the ROM 913 and theboot program of the magnetic disk device 920 are executed, and the BIOSprogram and boot program boot the operating system 921.

The programs 923 include a program that executes the function describedas a “part” (excluding the “storage part”; this applies to the followingexplanation as well) described in Embodiments 1 to 4. The program isread and executed by the CPU 911.

The files 924 store information, data, signal values, variable values,and parameters indicating the results of the processes described as“determining”, “checking”, “calculating”, “comparing”, “deriving”,“extracting”, “forming”, “updating”, “setting”, “registering”,“selecting”, and the like which are described in Embodiments 1 to 4, asthe items of “files” and “databases”.

The “files” and “databases” are stored in a recording medium such as adisk or memory. The information, data, signal values, variable values,and parameters stored in the storage medium such as the disk or memoryare read out to the main memory or cache memory by the CPU 911 through aread/write circuit, and are used for the operations of the CPU such asextraction, search, look-up, comparison, computation, calculation,process, edit, output, print, and display.

During the operations of the CPU including extraction, search, look-up,comparison, computation, calculation, process, edit, output, print, anddisplay, the information, data, signal values, variable values, andparameters are temporarily stored in the main memory, register, cachememory, buffer memory, or the like.

The arrows of the flowcharts described in Embodiments 1 to 4 mainlyindicate input/output of data and signals. The data and signal valuesare stored in a recording medium such as the memory of the RAM 914, theflexible disk of the FDD 904, the compact disk of the CDD 905, or themagnetic disk of the magnetic disk device 920; or an optical disk, minidisk, or DVD. The data and signals are transmitted online via the bus912, signal lines, cables, and other transmission media.

The “part” in Embodiments 1 to 4 may be a “circuit”, “device”, or“equipment”; or a “step”, “procedure”, or “process”. Namely, the “part”may be realized as the firmware stored in the ROM 913. Alternatively,the “part” may be practiced by only software; by only hardware such asan element, a device, a substrate, or a wiring line; by a combination ofsoftware and hardware; or furthermore by a combination of software,hardware, and firmware. The firmware and software are stored, asprograms, in a recording medium such as a magnetic disk, flexible disk,optical disk, compact disk, mini disk, or DVD. The program is read bythe CPU 911 and executed by the CPU 911. In other words, a programcauses the computer to function as a “part” in Embodiments 1 to 4.Alternatively, the program causes the computer to execute the procedureand method of the “part” in Embodiments 1 to 4.

In this manner, each of the certification device 101, authenticationdevice 102, and decryption device 103 indicated in Embodiments 1 to 4 isa computer comprising a CPU being a processing device; a memory,magnetic disk, or the like being a storage device; a keyboard, mouse,communication board, or the like being an input device; and a displaydevice, communication board, or the like being an output device, andrealizes the functions indicated as the “parts” by using theseprocessing device, storage device, input device, and output device, asdescribed above.

REFERENCE SIGNS LIST

101: certification device; 102: authentication device; 103: decryptiondevice; 201: biometric information extracting part; 202: feature vectorforming part; 203: random number generating part; 204: encrypting part:205: storage part; 206: communication part; 301: storage part; 302:encrypted similarity degree generating part; 303: checking part; 304:communication part; 305: random number generating part; 401: parametergenerating part; 402: decrypting part; 403: storage part; 404:communication part 404

1. A data processing device comprising: a public key storage part whichstores a public key generated in a decryption device based on a doublyhomomorphic encryption algorithm and distributed by the decryptiondevice; an encrypted data storage part which stores, as encrypted firstdata, first data that has been encrypted by an encryption device whichholds the public key distributed by the decryption device, by using thepublic key held in the encryption device; an encrypted data input partwhich, after the encrypted first data is stored in the encrypted datastorage part, inputs, as encrypted second data, second data that hasbeen encrypted by the encryption device by using the public key held inthe encryption device; a random number generating part which generates arandom number by using at least a part of the public key; and anencrypted similarity degree generating part which performs computationon the encrypted first data and the encrypted second data by using thepublic key stored in the public key storage part and the random numbergenerated by the random number generating part, and generates, asencrypted similarity degree information, encrypted information fromwhich a similarity degree between the first data and the second data canbe derived by a decryption process using a secret key generated tocorrespond to the public key, with the encrypted first data and theencrypted second data being kept encrypted.
 2. The data processingdevice according to claim 1, wherein the public key storage part storesthe public key generated by the decryption device to correspond to thesecret key based on the doubly homomorphic encryption algorithm, thedata processing device further comprising: an encrypted similaritydegree output part which outputs the encrypted similarity degreeinformation generated by the encrypted similarity degree generating partto the decryption device; a similarity degree input part which inputsthe similarity degree between the first data and the second data, thesimilarity degree being derived by performing, in the decryption device,a decryption process on the encrypted similarity degree information byusing the secret key; and a checking part which analyzes the similaritydegree inputted by the similarity degree input part and checks whetheror not a source of the second data is correct.
 3. The data processingdevice according to claim 1, wherein the encrypted data storage partstores encrypted first data constituted by T (T is an integer not lessthan 2) pieces of encrypted partial data which are obtained byencrypting, in the encryption device, T pieces of partial data thatconstitute the first data, wherein the encrypted data input part inputsencrypted second data constituted by T (T is an integer not less than 2)pieces of encrypted partial data which are obtained by encrypting, inthe encryption device, T pieces of partial data that constitute thesecond data, and wherein the encrypted similarity degree generating partperforms computation for each partial data of the encrypted first dataand encrypted second data by using the public key stored in the publickey storage part and the random number generated by the random numbergenerating part, and generates information from which the number ofpartial data, among the T pieces of partial data of the first data andthe T pieces of partial data of the second data, that have coincidentvalues can be derived, as the similarity degree between the first dataand second data.
 4. The data processing device according to claim I,wherein the encrypted data storage part stores encrypted first dataconstituted by T (T is an integer not less than 2) pieces of encryptedpartial data which are obtained by encrypting, in the encryption device,T pieces of partial data that constitute the first data, wherein theencrypted data input part inputs encrypted second data constituted by T(T is an integer not less than 2) pieces of encrypted partial data whichare obtained by encrypting, in the encryption device, T pieces ofpartial data that constitute the second data, and wherein the encryptedsimilarity degree generating part performs computation for each partialdata of the encrypted first data and encrypted second data by using thepublic key stored in the public key storage part and the random numbergenerated by the random number generating part, and generatesinformation from which a hamming distance between the T pieces ofpartial data of the first data and the T pieces of partial data of thesecond data can be derived, as the similarity degree between the firstdata and second data.
 5. The data processing device according to claim1, wherein the encrypted data storage part stores encrypted first dataconstituted by T (T is an integer not less than 2) pieces of encryptedpartial data which are obtained by encrypting, in the encryption device,T pieces of partial data that constitute the first data, wherein theencrypted data input part inputs encrypted second data constituted by T(T is an integer not less than 2) pieces of encrypted partial data whichare obtained by encrypting, in the encryption device, T pieces ofpartial data that constitute the second data, and wherein the encryptedsimilarity degree generating part performs computation for each partialdata of the encrypted first data and encrypted second data by using thepublic key stored in the public key storage part and the random numbergenerated by the random number generating part, and generatesinformation from which a Euclidean squared distance between the T piecesof partial data of the first data and the T pieces of partial data ofthe second data can be derived, as the similarity degree between thefirst data and second data.
 6. The data processing device according toclaim 1, wherein the public key storage part stores a public keygenerated based on the Okamoto-Takashima encryption algorithm, as thepublic key generated based on the doubly homomorphic encryptionalgorithm, wherein the encrypted data storage part stores encryptedfirst data obtained by encryption using the public key generated basedon the Okamoto-Takashima encryption algorithm, and wherein the encrypteddata input part inputs encrypted second data obtained by encryptionusing the public key generated based on the Okamoto-Takashima encryptionalgorithm.
 7. The data processing device according to claim 6, whereinthe public key storage part stores random bases w₁, w₂, w₃, ŵ₁, ŵ₂, ŵ₃generated to correspond to a secret key which is a regular matrix, and apredetermined value q, as the public key, wherein the encrypted datastorage part stores encrypted first data constituted by T (T is aninteger not less than 2) pieces of encrypted partial data ĉ_(i)(subscript i is 1 to T) which are obtained by encrypting T pieces ofpartial data b_(i) (subscript i is 1 to T) that constitute the firstdata, using the random bases w₁, w₂, and w₃, in the encryption devicethat holds the random bases w₁, w₂, and w₃, wherein the encrypted datainput part inputs encrypted second data constituted by T (T is aninteger not less than 2) pieces of encrypted partial data ĉ_(i)(subscript i is 1 to T) which are obtained by encrypting T pieces ofpartial data b′_(i) (subscript i is 1 to T) that constitute the seconddata, using the random bases ŵ₁, ŵ₂, and ŵ₃, in the encryption devicewhich holds the random bases ŵ₁, ŵ₂, and ŵ₃, wherein the random numbergenerating part generates a plurality of random number values s_(1,i),s_(2,i), s_(3,i), ŝ_(1,i), ŝ_(2,i), and ŝ_(3,i) (subscript i is 1 to T)based on the value q and generates a plurality of random number valuesu₂, u₃, û₂, and û₃ based on the value q, and wherein the encryptedsimilarity degree generating part calculatesd_(i)=c_(i)+(s_(1,i)×w₁)+(s_(2,i)×w₂)+(s_(3,i)×w₃) for 1 to T ofsubscript i, calculatesd̂_(i)=ĉ_(i)+(ŝ_(1,i)×ŵ₁)+(ŝ_(2,i)×ŵ₂)+(ŝ_(3,i)×ŵ₃) for 1 to T ofsubscript i, calculates E={a sum total of(ŝ_(1,i)×c_(i)+s_(1,i)×ŝ_(1,i)×w₁) for 1 to T of subscripti}+(u₂×w₂)+(u₃×w₃), calculates Ê={a sum total of (s_(1,i)×ĉ_(i)) for 1to T of subscript i}+(û₂×ŵ₂)+(û₃×ŵ₃), and generates encrypted similaritydegree information including the calculated values d_(i), d̂_(i), E, andÊ.
 8. The data processing device according to claim 7, wherein theencrypted data storage part stores encrypted first data constituted by Tpieces of partial data c_(i) which are obtained by encrypting T piecesof partial data b_(i) in accordance withc_(i)=(b_(i)×w₁)+(r_(2,i)×w₂)+(r_(3,i)×w_(3), by using random number values r)_(2,i) and r_(3,i) (subscript i is 1 to T) generated by the encryptiondevice, and the random bases w₁, w₂, and w₃, and wherein the encrypteddata input part inputs encrypted second data constituted by T pieces ofpartial data ĉ_(i) which are obtained by encrypting T pieces of partialdata b′_(i) in accordance withc_(i)=(b′_(i)×ŵ₁)+(r′_(2,i)×ŵ₂)+(r′_(3,i)×ŵ₃), by using random numbervalues r′_(2,i) and r′_(3,i) (subscript i is 1 to T) generated by theencryption device, and the random bases ŵ₁, ŵ₂, and ŵ₃.
 9. The dataprocessing device according to claim 7, further comprising: an encryptedsimilarity degree output part which outputs the encrypted similaritydegree information generated by the encrypted similarity degreegenerating part to the decryption device; a similarity degree input partwhich inputs a similarity degree between the first data and the seconddata, the similarity degree being derived by performing, in thedecryption device, a decryption process on the encrypted similaritydegree information by using an inverse matrix of the secret key and adistortion map in bilinear pairing vector spaces; and a checking partwhich analyzes the similarity degree inputted by the similarity degreeinput part, and checks whether or not a source of the second data iscorrect.
 10. The data processing device according to claim 6, whereinthe public key storage part stores random bases w₁, w₂, w₃, ŵ₁, ŵ₂ andŵ₃ generated to correspond to a secret key which is a regular matrix,and a predetermined value q, as the public key, wherein the encrypteddata storage part stores encrypted first data constituted by T (T is aninteger not less than 2) pieces of encrypted partial data c_(i)(subscript i is 1 to T) and T pieces of encrypted partial data ĉ_(i)(subscript i is 1 to T), the T pieces of encrypted partial data c_(i)being obtained by encrypting T pieces of partial data b_(i) (subscript iis 1 to T) that constitute the first data, using the random bases w₁,w₂, and w₃, in the encryption device which holds the random bases w₁,w₂, and w₃, and the T pieces of encrypted partial data ĉ_(i) (subscripti is 1 to T) being obtained by encrypting T pieces of partial data b_(i)that constitute the first data, using the random bases ŵ₁, ŵ₂, and ŵ₃,in the encryption device which holds the random bases ŵ₁, ŵ₂, and ŵ₃,wherein the encrypted data input part inputs encrypted second dataconstituted by T (T is an integer not less than 2) pieces of encryptedpartial data c′_(i) (subscript i is 1 to T) and T pieces of encryptedpartial data c′̂_(i) (subscript i is 1 to T), the T pieces of encryptedpartial data c′_(i) being obtained by encrypting T pieces of partialdata b′_(i) (subscript i is 1 to T) that constitute the second data,using the random bases w₁, w₂, and w₃, in the encryption device, and theT pieces of encrypted partial data c′̂_(i) being obtained by encrypting Tpieces of partial data b′_(i) that constitute the second data, using therandom bases ŵ₁, ŵ₂, and ŵ₃, in the encryption device, wherein therandom number generating part generates a plurality of random numbervalues s_(1,i), s_(2,i), ŝ_(3,i), ŝ_(1,i), ŝ_(2,i), and s^(̂) _(3,i)(subscript i is 1 to T) based on the value q and generates a pluralityof random number values u₂, u₃, û₂, and û₃ based on the value q, andwherein the encrypted similarity degree generating part calculatesd_(i)=(c_(i)−c′_(i))+(s_(1,i)×w₁)+(s_(2,i)×w₂)+(s_(3,i)×w₃) for 1 to Tof subscript i, calculates d̂_(i)=(ĉ_(i)−c′̂_(i))+(s^(̂) _(1,i)×ŵ₁)+(s^(̂)_(2,i)×ŵ₂)+(ŝ_(3,i)×ŵ₃) for 1 to T of subscript i, calculates E={a sumtotal of (ŝ_(1,i)×(c_(i)−c′_(i))+s_(1,i)×ŝ_(1,i)×w₁) for 1 to T ofsubscript i}+(u₂×w₂)+(u₃×w₃), calculates Ê=[a sum total of{(s_(1,i)×(ĉ_(i)−c′̂_(i))} for 1 to T of subscript i]+(û₂×ŵ₂)+(û₃×ŵ₃),and generates encrypted similarity degree information including thecalculated values d_(i), d̂_(i), E, and Ê.
 11. The data processing deviceaccording to claim 10, wherein the encrypted data storage part storesencrypted first data constituted by T pieces of partial data c_(i) and Tpieces of partial data ĉ_(i), the T pieces of partial data c_(i) beingobtained by encrypting T pieces of partial data b_(i) in accordance withc_(i)=(b_(i)×w₁)+(r_(2,i)×w₂)+(r_(3,i)×w₃) using random number valuesr_(2,i) and r_(3,i) (subscript i is 1 to T) generated by the encryptiondevice, and the random bases w₁, w₂, and w₃, and the T pieces of partialdata ĉ_(i) being obtained by encrypting T pieces of partial data b_(i)in accordance with ĉ_(i)=(b_(i)×ŵ₁)+(r^(̂) _(2,i)×ŵ₂)+(r̂_(3,i)×ŵ₃) usingrandom number values r̂_(2,i) and r̂_(3,i) (subscript i is 1 to T)generated by the encryption device, and the random bases ŵ₁, ŵ₂, and ŵ₃,wherein the encrypted data input part inputs encrypted second dataconstituted by T pieces of partial data c′_(i) and T pieces of partialdata c′̂_(i), the T pieces of partial data c′_(i) being obtained byencrypting T pieces of partial data b′_(i) in accordance withc′_(i)=(b′_(i)×w₁)+(r′_(2,i)×w₂)+(r′_(3,i)×w₃) using random numbervalues r′_(2,i) and r′_(3,i) (subscript i is 1 to T) generated by theencryption device, and the random bases w₁, w₂, and w₃, and the T piecesof partial data c′̂_(i) being obtained by encrypting T pieces of partialdata b′_(i) in accordance withc′̂_(i)=(b′_(i)×ŵ₁)+(r′̂_(2,i)×ŵ₂)+(r′_(3,i)×ŵ₃) using random numbervalues r′̂_(2,i) and r′̂_(3,i) (subscript i is 1 to T) generated by theencryption device, and the random bases ŵ₁, w^(̂) ₂, and ŵ₃.
 12. The dataprocessing device according to claim 10, further comprising: anencrypted similarity degree output part which outputs the encryptedsimilarity degree information generated by the encrypted similaritydegree generating part to the decryption device; a similarity degreeinput part which inputs the similarity degree between the first data andthe second data, the similarity degree being derived by performing, inthe decryption device, a decryption process on the encrypted similaritydegree information by using an inverse matrix of the secret key and adistortion map in bilinear pairing vector spaces; and a checking partwhich analyzes the similarity degree inputted by the similarity degreeinput part, and checks whether or not a source of the second data iscorrect.
 13. The data processing device according to claim 1, whereinthe public key storage part stores a public key generated based on theBGN (Boneh-Goh-Nissim) encryption algorithm, as the public key generatedbased on the doubly homomorphic encryption algorithm, and storesencrypted first data obtained by encryption using the public keygenerated based on the BGN encryption algorithm, and wherein theencrypted data input part inputs encrypted second data obtained byencryption using the public key generated based on the BGN encryptionalgorithm.
 14. The data processing device according to claim 13, whereinthe public key storage part stores a value g and a value u which areselected randomly from a group G having an order N=p×q (p and q areprimary numbers), a value h=u^(q), and a predetermined value N, as thepublic key, wherein the encrypted data storage part stores encryptedfirst data constituted by T (T is an integer not less than 2) pieces ofencrypted partial data c_(i) (subscript i is 1 to T) which are obtainedby encrypting T pieces of partial data b_(i) (subscript i is 1 to T)that constitute the first data, using the value g and the value h, inthe encryption device which holds the value g and the value h, whereinthe encrypted data input part inputs encrypted second data constitutedby T (T is an integer not less than 2) pieces of encrypted partial datac′_(i) (subscript i is 1 to T) which are obtained by encrypting T piecesof partial data b′_(i) (subscript i is 1 to T) that constitute thesecond data, using the value g and the value h, in the encryptiondevice, wherein the random number generating part generates a randomnumber value s based on the value N, and wherein the encryptedsimilarity degree generating part calculates an infinite productE=e(c_(i), c′₁)×e(g, h)^(s) for 1 to T of subscript i (e:G×Ĝ→G_(T) is apairing that satisfies bilinearity and non-degenerateness), andgenerates encrypted similarity degree information that includes thecalculated value E.
 15. The data processing device according to claim13, wherein the public key storage part stores a value g and a value uwhich are selected randomly from a group G having an order N=p×q (p andq are primary numbers), a value h=u^(q), and a predetermined value N, asthe public key, wherein the encrypted data storage part stores encryptedfirst data constituted by partial data c_(i) (subscript i is 1 to T)which are obtained by encrypting T (T is an integer not less than 2)pieces of partial data b_(i) (subscript i is 1 to T) that constitute thefirst data, using the value g and the value h, in the encryption devicewhich holds the value g and the value h, wherein the encrypted datainput part inputs encrypted second data constituted by T (T is aninteger not less than 2) pieces of encrypted partial data c′_(i)(subscript i is 1 to T) which are obtained by encrypting T pieces ofpartial data b′_(i) (subscript i is 1 to T) that constitute the seconddata, using the value g and the value h, in the encryption device,wherein the random number generating part generates a random numbervalue s based on the value N, and wherein the encrypted similaritydegree generating part calculates an infinite product E=e(c_(i),g)×e(c′_(i), g)×e(c_(i)×c′_(i))⁻²×e(g, h)^(s) for 1 to T of subscript i(e:G×Ĝ→G_(T) is a pairing that satisfies bilinearity andnon-degenerateness), and generates encrypted similarity degreeinformation that includes the calculated value E.